ABSTRACT: We study an extension of the model of Rubinstein (1993) to two ﬁrms, competing in a market with consumers who are boundedly rational with respect to processing information. The cognitive bound forces customers to partition the price space. Rubinstein shows that a monopolist is able to earn a higher proﬁt by exploiting consumers’ lack of processing ability. We extend his model to a duopoly, and show the Nash and Correlated equilibria of the game. We prove that in competition, whether ﬁrms choose their strategies independently or dependently, ﬁrms’ joint proﬁt is lower than in a monopoly but does not vanish completely. The uncertainty regarding the consumers’ cutoff point and differences across ﬁrms’ prices impel ﬁrms to set their prices equal to the marginal cost.